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Izvestiya: Mathematics, 2014, Volume 78, Issue 3, Pages 427–442
DOI: https://doi.org/10.1070/IM2014v078n03ABEH002692 (Mi im8035) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Modelling unsteady processes in semiconductors using a non-linear Sobolev equation

A. I. Aristov

M. V. Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics
English version PDF (260 kB) Citations (3)
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DOI: https://doi.org/10.1070/IM2014v078n03ABEH002692
Abstract: We study an initial-boundary value problem for a non-linear Sobolev equation containing a summand non-local in time and an inhomogeneity. The equation simulates unsteady processes in semiconductors. We find sufficient conditions for the unique solubility of the problem, both global in time and local (rather than global). In the case when the problem is soluble only locally, we find upper and lower bounds for the lifespan of a solution.
Keywords: equations of Sobolev type, blow-up of solutions, method of energy estimates.
Received: 11.07.2012
Revised: 23.09.2013
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2014, Volume 78, Issue 3, Pages 3–18
DOI: https://doi.org/10.4213/im8035
Bibliographic databases:
Document Type: Article
UDC: 517.955.8
MSC: Primary 35G31; Secondary 35B44
Language: English
Original paper language: Russian
Citation: A. I. Aristov, “Modelling unsteady processes in semiconductors using a non-linear Sobolev equation”, Izv. RAN. Ser. Mat., 78:3 (2014), 3–18; Izv. Math., 78:3 (2014), 427–442
Citation in format AMSBIB
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  • https://doi.org/10.1070/IM2014v078n03ABEH002692
  • https://www.mathnet.ru/eng/im/v78/i3/p3
    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:587
    Russian version PDF:196
    English version PDF:15
    References:49
    First page:60
     
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